Question

a university conducted a survey to understand credit card usage among its students. the students were categorized based on their year: first year, second year, and third year. the survey also distinguished between students who pay their credit card balance in full each month and those who carry a balance. the total number of students surveyed was 600.
given a student is a first year, what is the conditional relative frequency that they pay their credit card balance in full?

Explanation:

Step1: Recall the formula for conditional relative frequency

The formula for conditional relative frequency is \(P(A|B)=\frac{n(A\cap B)}{n(B)}\). Here, event \(A\) is "pay in full" and event \(B\) is "first - year student".

Step2: Identify the values from the table

From the table, \(n(A\cap B) = 120\) (the number of first - year students who pay in full) and \(n(B)=200\) (the total number of first - year students).

Step3: Calculate the conditional relative frequency

Substitute the values into the formula: \(\frac{120}{200}=0.6\)

Answer:

\(0.6\)